My question is this: Isn't it the case that LN only works well if there are lots of transactions in a channel? That is, if Alice sends 0.00001 BTC to Carol via Bob, and that's the only transaction in that channel in, say, a month, then benefits #2 & #3 above don't really apply since you effectively have a 1-to-1 relationship between a LN transaction and a blockchain transaction. Is that correct?
Correct.
However, there isn't necessarily any reason for Alice and Bob to close their channel, nor for Bob and Carol to close their channel.
Therefore, the channels could be left open for many years, allowing additional opportunities for Alice, Bob, and Carol to use the channels.
Additionally, if Alice, Bob, or Carol are well connected enough, then all three of them could continue to use those same channels for other payments to other Lightning Network users elsewhere on the network.